A330428 Smallest prime p such that both nearest primes up and down are farther away than n*log(p).

5, 211, 38501, 413353, 10938023, 142414669, 163710121, 8835528511, 31587561361, 343834606051, 1480975873513, 26923643849953

Offset: 1

Author

Steven M. Altschuld, Dec 14 2019

Keywords

• nonn
• more
• hard

Comments

For these numbers, the name "Lowest Frogger Primes" LFP(n) is suggested because (frog) jumps with a length greater than n times the local average are required to bridge the gaps (logs).

Crossrefs

Cf. A288908 (with 1*log(P)), A330426 (with 2*log(P)), A330427 (with 3*log(P)).

Cf. A023186, A120937.

Programs

PARI

{my(npp=2,np=3,n=1);forprime(p=5,10^9,my(d=log(p)*n);if(np-npp>d&&p-np>d,print(np,", ");n++);npp=np;np=p)} \\ Hugo Pfoertner, Dec 14 2019

Extensions

a(5)-a(9) from Hugo Pfoertner, Dec 14 2019

a(10) from Hugo Pfoertner, Dec 16 2019

a(11)-a(12) from Giovanni Resta, Dec 19 2019